The Reactivation and Nucleus Characterization of Main-belt Comet 358P/PANSTARRS (P/2012 T1)

During the course of computing the best-fit phase function of 358P using data acquired in 2017 when the object was apparently inactive (Section 3.1), we noted that photometric points from 2017 November 18 and December 18 appeared to be significantly brighter than expected (by ≥1 mag) relative to the best-fit function found using only the other data points from 2017 July 1 through 2017 October 26. A possible faint, short dust tail extending ∼1–2 arcsec roughly eastward, close to the antisolar direction, is also barely visible in the composite image from December (Figure 2(h)). Careful examination of individual and composite image data did not show any indications of this photometry or observed morphology being contaminated by underlying faint field stars or nearby bright field stars. The observed photometric deviations are well outside the range of expected rotational variation for the object assuming a physically plausible axis ratio for the nucleus (cf. Figure 3). Measurements of the full width at half-maximum (FWHM) of the PSFs of the object and nearby field stars did not give any indications of the presence of resolved coma.

To verify the visual detection of activity from 358P on 2017 December 18, we analyze the surface-brightness profile of the object on that date. To do so, we create a composite image constructed by shifting and aligning individual images on the photocenter of a reference star in each frame, where the reference star is chosen based on its proximity to our target object, the fact that it is relatively bright without being saturated, and the absence of other nearby background sources. This star-aligned composite image and the object-aligned composite image from the same date (Section 2; Figure 2) are rotated by the same angle such that star trails are horizontal in each image frame.

We then construct one-dimensional surface-brightness profiles oriented along an axis (marked by blue and red arrows superimposed on unrotated composite images of the object and reference star in Figures 4(a) and (b)) perpendicular to the direction of the non-sidereal motion of the object. We measure profiles along this direction because it allows us to directly compare results from images of the object and reference star in a manner that cannot be done along different axes (e.g., the one aligned with the apparent dust tail) due to the trailing of field stars caused by non-sidereal tracking of the telescope to follow the target during the acquisition of these images.

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A series of horizontal rectangular apertures are placed along the vertical axes of the rotated images of the object and reference star, where each aperture is one pixel high and the width of the apertures is chosen such that ∼90% of the flux from the source along the horizontal row passing through each source's photocenter is encompassed by the aperture along that central row. We measure average fluxes within these rectangular apertures, and subtract sky background sampled from nearby areas of blank sky.

We normalize the profiles of 358P and the reference star to unity at their peaks and plot them together (Figure 4). Significant excess flux in the direction of the suspected faint dust tail can be clearly seen in the wings of the object profile relative to the stellar profile (while we also see, as noted above, that the FWHMs of the object and stellar profiles are nearly identical).

As can be seen in Figure 4, the requirement that our one-dimensional surface-brightness profiles be measured along the axis perpendicular to the non-sidereal velocity vector of the object means that we do not measure the profile along the axis of the apparent dust tail, along which the maximum deviation from a stellar PSF is expected. As such, the excess flux in the object PSF relative to the stellar PSF shown in Figure 4 should be regarded as a lower limit to the true amount of excess flux present in the object's PSF compared to that of an inactive, point-source-like object.

The S/N of the object detection in our 2017 November 18 data is too low to obtain a useful surface-brightness profile and perform a similar analysis as described above for our 2017 December 18 data. As such, we cannot independently corroborate our photometric detection of activity on that date described above. Nonetheless, based on the photometric indication of activity for our 2017 November 18 data and confirmation of activity via surface-brightness profile analysis for our 2017 December 18 data, we conclude that 358P has become active again. Subtracting the expected brightness of the nucleus from the actual total measured brightness of the object at the time of observations and averaging over a photometry aperture encompassing the visible flux from the object and its apparent dust tail, we estimate the average surface brightness of the tail and any coma that may be present to be Σ_d ∼ 26.5 mag arcsec².

Using the phase function derived earlier, we can estimate the amounts of excess dust present in observations from 2012 and 2013 reported by Hsieh et al. (2013), and in 2017 reported in this work. Following Hsieh (2014), we estimate the total scattering surface area, A_d, of visible ejected dust using

$$\begin{eqnarray}&&{A}_{d}=\pi {r}_{N}^{2}\left(\displaystyle \frac{1-{10}^{0.4({H}_{R,t}-{H}_{R})}}{{10}^{0.4({H}_{R,t}-{H}_{R})}}\right)\end{eqnarray} \tag{ 3 }$$

and the corresponding total mass, M_d, using

$$\begin{eqnarray}&&{M}_{d}=\displaystyle \frac{4}{3}\pi {r}_{N}^{2}\bar{a}{\rho }_{d}\left(\displaystyle \frac{1-{10}^{0.4({H}_{R,t}-{H}_{R})}}{{10}^{0.4({H}_{R,t}-{H}_{R})}}\right)\end{eqnarray} \tag{ 4 }$$

where H_R,tot is the equivalent total absolute magnitude of the active nucleus at R = Δ = 1 au and α = 0° computed using the H, G phase function and the best-fit G parameter determined above (Section 3.1; assuming that the dust exhibits the same phase-darkening behavior as the nucleus). We assume dust grain densities of ρ_d = 2500 kg m⁻³, consistent with CI and CM carbonaceous chondrites, which are associated with primitive C-type objects like the MBCs (Britt et al. 2002).

Moreno et al. (2013) found dust grain radii for 358P's observed dust emission in 2012 ranging from a_d,min = 0.5 μm (although they report that this lower limit is not well-constrained) to a_d,max = 1−10 cm, assuming a power law size distribution with an index of q = 3.5. Following Jewitt et al. (2014), we can compute a mean effective particle radius (by mass), ${\bar{a}}_{d}$, weighted by the size distribution, scattering cross-section, and residence time, and assuming a_d,max ≫ a_d,min, using

$$\begin{eqnarray}&&{\bar{a}}_{d}\sim \displaystyle \frac{{a}_{d,\max }}{\mathrm{ln}({a}_{d,\max }/{a}_{d,\min })}.\end{eqnarray} \tag{ 5 }$$

Using the particle size distribution determined by Moreno et al. (2013), we obtain ${\bar{a}}_{d}=1$−10 mm, where for the purposes of our following analysis, we will use ${\bar{a}}_{d}=1\,\mathrm{mm}$.

For reference, we also compute A(α = 0°)fρ values (hereafter, Afρ; A'Hearn et al. 1995), given by

$$\begin{eqnarray}&&{Af}\rho =\displaystyle \frac{{(2R{\rm{\Delta }})}^{2}}{\rho }{10}^{0.4[{m}_{\odot }-{m}_{R,d}(R,{\rm{\Delta }},0)]}\end{eqnarray} \tag{ 6 }$$

where R is in au, Δ is in cm, ρ is the physical radius in cm of the photometry aperture used to measure the magnitude of the comet at the distance of the comet, and m_R,d(R, Δ, 0) is the phase-angle-corrected (to α = 0°, assuming the same H,G phase function behavior for the dust as for the nucleus) R-band magnitude of the excess dust mass of the comet (i.e., with the flux contribution of the nucleus subtracted from the measured total magnitude). We note, however, that this parameter is not always a reliable measurement of the dust contribution to comet photometry in cases of nonspherically symmetric comae (e.g., Fink & Rubin 2012).

The results of all calculations described above are shown in Table 2 for observations of 358P from Hsieh et al. (2013) and this work. We also plot total absolute magnitudes and computed excess dust masses as functions of true anomaly, ν, and days relative to perihelion in Figure 5.

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We fit a linear function to the two data points from 2017 when the object appears to be active, aiming to estimate the average dust production rate of the object over this period (represented by the slope of this function) and the start time of its activity. For reference, the object's heliocentric distance changes from R = 2.522 au to R = 2.479 au between the two dates at which those data points were acquired. This heliocentric distance change corresponds to a ∼5%–20% increase in the water sublimation rate on the object's surface, depending on whether the isothermal or subsolar approximation is assumed (following the calculations detailed by Hsieh et al. 2015a). The resulting dust production rate and corresponding activity start date we find are of course subject to numerous sources of uncertainty including the nonlinearity of the actual dust production rate as a function of heliocentric distance, ordinary photometric calibration uncertainties, uncertainties specifically associated with measuring extended objects (e.g., selection of optimal photometry apertures), and the unknown rotational phases of the object at the times when each photometric point was obtained.

Although the rotational phases of the object at the time of our 2017 November and December observations are unknown, we can estimate the uncertainty that the nucleus's rotational light curve imparts on our photometry given the amount of unresolved coma dust (which will tend to damp the amplitude of observed rotational brightness variations) that we have calculated to be present at those times. The implied minimum axis ratio (neglecting possible projection effects), (a/b)_N, for an object with a rotational light curve with a measured or assumed peak-to-trough photometric range, Δm_R, is given by

$$\begin{eqnarray}&&{\left(\displaystyle \frac{a}{b}\right)}_{N}={10}^{0.4{\rm{\Delta }}{m}_{R}}.\end{eqnarray} \tag{ 7 }$$

The underlying axis ratio of the nucleus of an active object including coma dust within a given photometry aperture can be computed using

$$\begin{eqnarray}&&{\left(\displaystyle \frac{a}{b}\right)}_{N}+\displaystyle \frac{{F}_{d}}{{F}_{N}}(1-{10}^{0.4{\rm{\Delta }}{m}_{\mathrm{obs}}}){\left(\displaystyle \frac{a}{b}\right)}_{N}^{1/2}-{10}^{0.4{\rm{\Delta }}{m}_{\mathrm{obs}}}=0\end{eqnarray} \tag{ 8 }$$

where Δm_obs is the observed peak-to-trough photometric range, and F_d/F_N is the computed dust-to-nucleus flux ratio. This equation can be solved for $(a/b{)}_{N}^{1/2}$ using standard techniques for solving quadratic polynomials (Hsieh et al. 2011a), where F_d/F_N = A_d/A_N and ${A}_{N}=\pi {r}_{N}^{2}=3\times {10}^{5}$ m² for 358P. Rearranging Equation (8), we can solve for the expected observed photometric range for an object with a known or assumed nucleus axis ratio and measured dust-to-nucleus flux ratio using

$$\begin{eqnarray}&&{\rm{\Delta }}{m}_{\mathrm{obs}}=2.5\mathrm{log}\left(\displaystyle \frac{{\left(\tfrac{a}{b}\right)}_{N}+{\left(\tfrac{a}{b}\right)}_{N}^{1/2}\left(\tfrac{{F}_{d}}{{F}_{N}}\right)}{1+{\left(\tfrac{a}{b}\right)}_{N}^{1/2}\left(\tfrac{{F}_{d}}{{F}_{N}}\right)}\right).\end{eqnarray} \tag{ 9 }$$

Assuming the same light-curve amplitude of A_N = 0.30 mag (corresponding to Δm_R = 0.60 mag) for 358P's nucleus that we used earlier (Section 3.1) and the estimated total scattering surface areas of dust in Table 2, we then find Δm_obs = 0.24 mag (corresponding to an expected observed amplitude of A_obs = 0.12 mag), for the nucleus on 2017 November 18 and Δm_obs = 0.09 mag (corresponding to A_obs = 0.05 mag) on 2017 December 18. We therefore find that for a reasonable assumed axis ratio for 358P's nucleus, light-curve amplitude damping by coma material should reduce potential rotational brightness variations to comparable or negligible levels relative to measured photometric uncertainties and uncertainties on our best-fit values for H_R and G_R that are used to compute M_d via Equation (4). We also conclude that any photometric fluctuations observed for 358P in observations obtained in 2012 and 2013, when inferred excess dust masses were much larger than in 2017, are unlikely to be due to nucleus rotation and more likely to be due to observational effects such as seeing fluctuations causing fluctuations in the amount of dust contained within fixed photometry apertures from one image to the next. Given the slow dust ejection speeds found for most MBCs (e.g., Hsieh et al. 2004, 2009b, 2011a; Moreno et al. 2011, 2016), we do not expect rotational variations in dust production rates to cause significant fluctuations in measured photometry from ground-based data.

Using the uncertainties we originally calculated for the dust masses measured for 2017 November 18 and December 18, we estimate an average dust production rate shortly after 358P becomes active of $\dot{M}=2.0\pm 0.6$ kg s⁻¹ (roughly consistent with the average dust production rate found for the object in 2012 by Moreno et al. 2013) and an estimated start date of 155 ± 4 days prior to perihelion. This start date corresponds to 2017 November 8 ± 4 when the object was at ν = 3161 ± 09, or equivalently, ν = −439 ± 09, and at R = 2.538 au.

For reference, we perform a simple dust modeling analysis to determine whether the start date we estimate from the object's dust mass evolution is consistent with the activity that we visually detect in our 2017 December 18 observations. Using an online tool¹² developed by J. B. Vincent for plotting syndyne and synchrone grids (Finson & Probstein 1968), we find that a_d ∼ 1 mm dust grains ejected with zero initial velocity and evolving under the influence of solar gravity and solar radiation pressure would be expected to travel ∼1 arcsec from the nucleus in the antisolar direction in 40 days (the length of time elapsed between our estimate for the start date of the activity and the observations in question). Slightly smaller dust grains (a_d ∼ 100 μm) would be expected to travel about 7 arcsec from the nucleus in the same direction over the same period of time. Given that the dust ejected by 358P likely contains a range of dust particle sizes, and not just the mean particle size of ${\bar{a}}_{d}=1\,\mathrm{mm}$ that we use above for our dust mass calculations, we find that these dust modeling results are fully consistent with our observations of a ∼1–2 arcsec antisolar dust tail on 2017 December 18 and our estimated start date of 2017 November 8 ± 4 for the current active period. More detailed dust modeling is not justified at this time due to the minimal amount of data presently available for 358P's current active period, although it is planned in the upcoming year once more data can be obtained during the object's next available observing window (see below).

Observations when the object is active in 2012–2013 and 2017 do not overlap in true anomaly, and so it is not possible at this time to compare activity levels from the different active epochs to ascertain how much activity attenuation, if any, has taken place. From Figure 5, it appears possible that if the initial dust production rate estimated for 358P in 2017 is assumed (likely incorrectly) to be maintained at a constant level at later times, a similar amount of total dust (within uncertainties) could be ejected by the object during its current active period as was measured during its 2012–2013 active period. Detailed dust modeling or comparison of observations from both epochs covering overlapping orbit arcs (or ideally both) are needed, however, to robustly compare the strength of the activity observed during each epoch. Both of these tasks will be the focus of future work, subject to the acquisition of new observations during 358P's next upcoming observing window.

358P is next observable from 2018 August until 2019 May, during which it will cover a true anomaly range of 30° ≲ ν ≲ 100°, where observability will be best at Northern Hemisphere sites. This observing window should allow for the acquisition of observations that will overlap the latter portion of the orbital arc covered by previously reported 2012–2013 data and that should also help constrain the rate of fading of residual activity from the object as it approaches aphelion. Observations of the object are highly encouraged during this period.